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Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.

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Title: Fault tolerability analysis of hypercubes based on the [formula omitted]-cyclic fault pattern.
Authors: Tian, Ting1 (AUTHOR) tianting1201@163.com, Zhang, Shumin1,2,3 (AUTHOR) zhangshumin@qhnu.edu.cn, Zhu, Bo1 (AUTHOR) zhuboqh@163.com, Chang, Jou-Ming4 (AUTHOR) spade@ntub.edu.tw
Source: Discrete Applied Mathematics. Jun2026, Vol. 386, p293-305. 13p.
Subjects: Hypercubes, Graph connectivity, Graph theory, Computer network architectures, Fault tolerance (Engineering)
Abstract: The connectivity of a graph and its various generalizations have been extensively studied due to their significant impact on fault tolerance in interconnection networks. In this paper, we further elaborate on the concept of cyclic connectivity and propose a novel form of it. Given a connected graph G = (V (G) , E (G)) and an integer g ≥ 1 , a g -cyclic vertex cut of G is a vertex subset S ⊆ V (G) such that G − S is disconnected and there are at least g + 1 components containing cycles. The g -cyclic connectivity of G , denoted by κ c g (G) , is defined as the cardinality of a minimum g -cyclic vertex cut of G. Then, we derive an upper bound for the g -cyclic connectivity of the n -dimensional hypercube Q n. Specifically, κ c g (Q n) ≤ 4 g (n − 2) − 2 g (g + 1) + 4 for n ≥ 4 and 1 ≤ g ≤ n − 3. Moreover, we determine the exact g -cyclic connectivity of Q n as κ c g (Q n) = 4 g (n − 2) − 2 g (g + 1) + 4 for g ∈ { 1 , 2 , 3 } when n is sufficiently large. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:The connectivity of a graph and its various generalizations have been extensively studied due to their significant impact on fault tolerance in interconnection networks. In this paper, we further elaborate on the concept of cyclic connectivity and propose a novel form of it. Given a connected graph G = (V (G) , E (G)) and an integer g ≥ 1 , a g -cyclic vertex cut of G is a vertex subset S ⊆ V (G) such that G − S is disconnected and there are at least g + 1 components containing cycles. The g -cyclic connectivity of G , denoted by κ c g (G) , is defined as the cardinality of a minimum g -cyclic vertex cut of G. Then, we derive an upper bound for the g -cyclic connectivity of the n -dimensional hypercube Q n. Specifically, κ c g (Q n) ≤ 4 g (n − 2) − 2 g (g + 1) + 4 for n ≥ 4 and 1 ≤ g ≤ n − 3. Moreover, we determine the exact g -cyclic connectivity of Q n as κ c g (Q n) = 4 g (n − 2) − 2 g (g + 1) + 4 for g ∈ { 1 , 2 , 3 } when n is sufficiently large. [ABSTRACT FROM AUTHOR]
ISSN:0166218X
DOI:10.1016/j.dam.2026.02.013